Finite Group Databasebeta

← #30599223

Subgroups — #30599223

Order 15616.

830 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461642C211yesmaximal, characteristic
2#21461642C211yesmaximal, characteristic
3#21460657C214yesmaximal, complemented
4C2×#16839619C211yesmaximal, characteristic
5C2×#14519834—21no—
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×C22⋊#92420C2212yes—
10C2×C22⋊#92420C2212yes—
11C23×C4×D61C2211yescharacteristic
12C22×C4⋊Dic61C411yescharacteristic
13C22×#11758198C412yes—
14#16839619—21no—
15#16839619—21no—
16#16839619—21no—
17#16839619—21no—
18C2×#14519684C2212yes—
19C22×C4⋊C4×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519834—42no—
23#14519834—42no—
24#14519834—42no—
25#14519834—42no—
26C22⋊#92420—24no—
27C22⋊#92420—24no—
28C24×D61C2×C411yescharacteristic
29C23×Dic61C2×C412yes—
30C23×Dic61C2311yescharacteristic
31C22×C4×D61—24no—
32C22×C4×D61—42no—
33C22×C4×D61—42no—
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—42no—
41C2×#11758198—22no—
42C2×#11758198—22no—
43C2×#11758198—44no—
44#14519684—22no—
45#14519684—22no—
46C23×C4×C61C2×C412yes—
47C23×C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—42no—
51C24×C61C22×C411yescharacteristic
52C23×D61—22no—
53C23×D61—22no—
54C23×D61—22no—
55C23×D61—22no—
56C23×D61—22no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61C22⋊C411yescharacteristic
60C23×D61C22⋊C411yescharacteristic
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—24no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×Dic61—22no—
71C22×Dic61—24no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61#4114yes—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—416no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C4⋊C4×C61—42no—
99C4⋊C4×C61—42no—
100#11758198—44no—
101#11758198—44no—
102C4⋊Dic61—42no—
103C4⋊Dic61—42no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61#11712yes—
110C23×C61#13112yes—
111C23×C61#13112yes—
112C22×D61—28no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—44no—
126C22×D61—44no—
127C22×D61—44no—
128C22×D61—44no—
129C22×D61—44no—
130C22×D61—44no—
131C22×D61#10012yes—
132C22×D61#10112yes—
133C2×C4×C61—28no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—84no—
142C2×C4×C61#9912yes—
143C2×C4×C61#9912yes—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—44no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—84no—
153C2×Dic61#12312yes—
154C2×Dic61#12312yes—
155C4×D61—44no—
156C4×D61—44no—
157C4×D61—44no—
158C4×D61—44no—
159#92420—82no—
160#92420—82no—
161#8704—611nomaximal, Sylow
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61#38111yescharacteristic
169C22×C61#40811yescharacteristic
170C22×C61#40811yescharacteristic
171C22×C61C2×#9911yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C22×C61C2×#10011yescharacteristic
174C22×C61C2×#10111yescharacteristic
175C22×C61#43314yes—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—416no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C4×C61—22no—
192C4×C61—22no—
193C4×C61—82no—
194Dic61—22no—
195Dic61—22no—
196Dic61—82no—
197C2×#380—611no—
198#1779—611no—
199#1779—611no—
200#1280—614no—
201C2×C61—24no—
202C2×C61#147111yescharacteristic
203C2×C61#147111yescharacteristic
204C2×C61#147211yescharacteristic
205C2×C61#147211yescharacteristic
206C2×C61#181811yescharacteristic
207C2×C61#181911yescharacteristic
208C2×C61#182111yescharacteristic
209D61—42no—
210D61—42no—
211C24×C4—611no—
212C22×C4⋊C4—611no—
213C22×C4⋊C4#692311yescharacteristic
214C22×C22⋊C4—612no—
215C2×C22⋊C8—612no—
216C2×C22⋊C8—612no—
217C2×C22⋊C8—1221no—
218C2×C22⋊C8—1221no—
219C2×C22⋊C8—1221no—
220C2×C22⋊C8—1221no—
221#380—1221no—
222#380—1221no—
223#380—1221no—
224#380—1221no—
225C2×#95—612no—
226C61#870411yescharacteristic, complemented, Sylow
227C25—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—612no—
234C23×C4—1224no—
235C23×C4—2442no—
236C23×C4—2442no—
237C23×C4C2×#692312yes—
238C23×C4C2×#692311yescharacteristic
239C22×C8—1222no—
240C22×C8—1222no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—2442no—
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—1222no—
249C2×C22⋊C4—2444no—
250C22⋊C8—1224no—
251C22⋊C8—1224no—
252C22⋊C8—2442no—
253C22⋊C8—2442no—
254C22⋊C8—2442no—
255C22⋊C8—2442no—
256#95—1222no—
257#95—1222no—
258C24—611no—
259C24—611no—
260C24—1222no—
261C24—1222no—
262C24—1222no—
263C24—1222no—
264C24—1222no—
265C24—2441no—
266C24—2441no—
267C24C22×#692311yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—614no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—1224no—
287C22×C4—1222no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—24416no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22⋊#692311yescharacteristic
299C2×C8—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C2×C8—2442no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—2442no—
308C4⋊C4—2442no—
309C22⋊C4—2444no—
310C22⋊C4—2444no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—612no—
316C23—612no—
317C23—1228no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—2444no—
331C23—2444no—
332C23—2444no—
333C23—2444no—
334C23—2444no—
335C23—2444no—
336C23C2×C22⋊#692311yescharacteristic
337C23#1451985612yes—
338C23#1451986412yes—
339C23#1451986512yes—
340C2×C4—28no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—84no—
349C2×C4—612no—
350C2×C4—612no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—4884no—
356C2×C4—2444no—
357C2×C4—2444no—
358C2×C4—2444no—
359C2×C4—2444no—
360C2×C4—2444no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4#1451983512yes—
365C2×C4#1451983612yes—
366C8—4882no—
367C8—4882no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—1222no—
378C22—1222no—
379C22—1222no—
380C22—24416no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22#1684070511yescharacteristic
390C22#1684073611yescharacteristic
391C22#1684073711yescharacteristic
392C22C2×#1451983511yescharacteristic
393C22C2×#1451983611yescharacteristic
394C22D61⋊#10011yescharacteristic
395C22D61⋊#10111yescharacteristic
396C22#1684078714yes—
397C4—22no—
398C4—22no—
399C4—82no—
400C4—1222no—
401C4—1222no—
402C4—4882no—
403C2—24no—
404C2—2442no—
405C2—2442no—
406C2#2146109411yescharacteristic
407C2#2146109611yescharacteristic
408C2#2146109711yescharacteristic
409C2#2146109911yescharacteristic
410C2#2146171311yescharacteristic
411C2#2146171411yescharacteristic
412C2#2146171911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8704
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21460657C2semidirect
226. C61#8704semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214616422
#214606572
C2×#168396192
#870461